Math 5520
– Introduction to Topology
Spring
2023
Instructor: Ken
Bromberg
Office: JWB 303
Email:
bromberg@math.utah.edu
Office hours: M 2-3,Th 2- 3:30 and by appointment
Course description:
This course is the second semester of an introduction to topology and geometry. We will cover the fundamental group and covering spaces following the course notes. My goal in the course is not to maximize the number of topics we cover but rather focus on understanding well a smaller number of topics. Most students find the material in this course very different than anything they've seen before.
Prerequisites: “C”
or better in Math 5510 or consent of the instructor. Math 5310 will also be helpful but not required. Meeting place and time: MWF
9:40-10:30, JWB 208 Text: We will follow these course notes. They will be regularly updated. The textbook from 5510, Topology
by James Munkres is also a good reference. Homework: Due Jan. 20, 10 pm Problems 1,3,5,7
All problems are from the notes (unless otherwise stated).
Due Feb. 1, 10 pm
Problem
Due Feb 13, 10 pm
Problems 11,12,13,14
Due Feb 24, 10 pm
You should do and hand in the problems from the topology worksheet.
You can use the problems from the algebra worksheet.
Solutions
Due Mar 14, 10 pm
Problems 15, 16, 17, 18, 19
Due Mar 29, 10 pm
Problems 20, 21, 22, 23
Due Apr 12, 10 pm
Worksheet
Due Apr 27, 10 pm
Problems 24, 30, 31
Quizzes: There will be 4 quizzes. Tentatively they will be on Feb. 3, Feb. 24, Mar. 24, and Apr. 14. Each quiz will be 20 minutes and I will give them at the end of class. I will drop your lowest quiz score.
Final: The final exam is on Wednesday, May 3rd from 8:00-10:00 AM. It will be a comprehensive exam.
Grades: I plan on assigning around 10 homework sets (approximately due ever week and a half). You will be required to submit your answers in LaTeX. Homework will be 50% of your grade, quizzes 25% and the final 25%.
University Policies
The Americans with Disabilities Act. The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in this class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, (801) 581-5020. CDS will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services.
University Safety Statement. The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit safeu.utah.edu.
Addressing Sexual Misconduct. Title IX makes it clear that violence and harassment based on sex and gender (which Includes sexual orientation and gender identity/expression) is a civil rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran’s status or genetic information. If you or someone you know has been harassed or assaulted, you are encouraged to report it to the Title IX Coordinator in the Office of Equal Opportunity and Affirmative Action, 135 Park Building, 801-581-8365, or the Office of the Dean of Students, 270 Union Building, 801-581-7066. For support and confidential consultation, contact the Center for Student Wellness, 426 SSB, 801-581-7776. To report to the police, contact the Department of Public Safety, 801-585-2677(COPS).
Undocumented Student Support Statement. Immigration is a complex phenomenon with broad impact—those who are directly affected by it, as well as those who are indirectly affected by their relationships with family members, friends, and loved ones. If your immigration status presents obstacles to engaging in specific activities or fulfilling specific course criteria, confidential arrangements may be requested from the Dream Center. Arrangements with the Dream Center will not jeopardize your student status, your financial aid, or any other part of your residence. The Dream Center offers a wide range of resources to support undocumented students (with and without DACA) as well as students from mixed-status families. To learn more, please contact the Dream Center at 801.213.3697 or visit dream.utah.edu.